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What is the length, x, of your shadow shadow as you walk to the right and the angle, , , to the lamp decreases? x

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shadow What is the length, x, of your shadow as you walk to the right and the angle, , to the lamp decreases? x

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x

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x

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x Assume you are 2m tall: 2

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x 2

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I can picture the relationship between and tan( ). But what does 1/tan( ) relationship look like?

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1/tan( ) looks like this, and is called the cotangent. Notice as the angle gets closer and closer to zero, the length of your shadow approaches infinity.

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So 2/tan( ) looks like this. When the angle is 90 , you have zero shadow; when the angle is 45 , you have a shadow of 2m, when the angle is 15 , your shadow is approx 20m long.

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Notice how like any reciprocal function, all values of the function in the band ‘0 to 1’ get stretched to the ‘greater than one band’; all values greater than one get compressed into the ‘zero to one’ band. Same for the negative bands too. Reciprocal of a line

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You can survive without cotangent, and secant, and cosecant. But their graphs make picturing typical problems in daily life easier. In fact you can survive with only ‘sine’ if necessary, all the other trigonometric functions are just for you to better picture relationships between angles and some other related value.

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